How GSEs and Marking to Market Accounting Created and Spread the Subprime Crisis and What to do About it
This paper was part of a larger project done with Josh Graver and Kelly Raven for the Financial Engineering Course. Thanks both for your help and support.
December 4, 2008
FOR THE FINANCIAL ENGINEERING PROSEMINAR COURSE AT
MIT SLOAN SCHOOL OF MANAGEMENT
This paper explores the role of Government Sponsored Enterprises (GSEs) and accounting standards in the crisis.
We find that because of their special borrowing costs and capital requirements GSEs (especially Fannie and Freddie) greatly contributed to creating this crisis by artificially inflating the price of residential housing. We think it is the first time the GSEs impact on this crisis is quantified. One of our recommendations is that special privileges of these GSEs should be eliminated.
We also analyze the impact of accounting regimes in this crisis. We agree with many of the academic research that has been done in this field, that Marking to Market accounting is a cause for the contagion of the housing crisis to the rest of the financial system and the economy. We also find, for the first time as far as we know, that the Heisenberg’s Uncertainty Principle, well known in physics, can be applied to financial markets in the sense that by measuring the value in the market, we are changing the value and thus incurring in losses. In regard to accounting standards we recommend using Historical Cost accounting and dropping Marking to Market accounting.
We specially thank Professor Mark Kritzman for his time and guidance throughout the project. We also thank Greg Hawkins of Citigroup for his participation in the Financial Engineering Proseminar and for his continuing support, insights and time. We also thank MIT and MIT Sloan for their financial support.
PART II: THE HOUSING CRISIS
1- Explaining the Crisis: The three Hypotheses
There are three hypotheses to explain the housing bubble: the income hypothesis, the supply side hypothesis and the price expectation hypothesis. These were analyzed and tested in The Consequences of Mortgage Credit Expansion: Evidence from the U.S. Mortgage Default Crisis (Mian & Sufi 2008, University of Chicago).
· A. Income Hypothesis
This hypothesis suggests causality between income growth and an increase in borrowing and housing prices. While this hypothesis is appealing, Mian & Sufi observed that mortgage origination is stronger in areas where real income is falling. Further, 2002-2005 is the only period in the past 18 years when credit growth has been negatively correlated with income growth. Finally, it is argued that if income was the main driver of credit then borrowing increases would be observed for all types of debt, not mortgages alone, while this has not historically been the case.
Another argument in favor of the income hypothesis is that the business cycle (decline in risk free rate) favors borrowers and thus drives credit and prices. However, this does not consider that housing prices adjust to the lower cost of credit which increases the principal to be paid by the borrower. Moreover, this ignores the fact that the drop in the risk free rate in the early nineties was not followed by such an increase in mortgages.
· B. House Price Expectation Hypothesis
Under this hypothesis, the increase in expected housing prices is at the source of the increase in borrowing. If this is true, there should be no credit growth in areas where there is high housing supply elasticity given that any increase in price would be compensated for by an increase in supply and would keep prices stable. By comparing samples of highly elastic and highly inelastic housing supplies, Mian & Sufi proved that price expectations do not play a role in the increase of credit.
· C. Securitization and Credit Rating Agencies Hypothesis
Securitization is a mechanism that increases the speed at which money is transferred in the economy and thus creates liquidity. However, the securitization wave began in 2002 and the price boom began in 1999 (when the Shiller index grew by 10%), continued in 2000 (14% growth) and was only interrupted in 2001 with the 9-11 shock and the subsequent recession (see Figure 1).
Another argument against the securitization hypothesis is that securitization also occurs in other markets, including commercial mortgage, auto loans, student loans, and credit card receivables. If securitization were to blame for the housing bubble, similar effects should have been observed in these securitized assets.
Figure 1: Case Shiller Index
1- How Fannie Mae and Freddie Mac Contributed to the Housing Crisis
Thus far we have discarded the income, expectations and securitizations hypotheses, and the question remains as to what caused housing bubble. The team hypothesizes that excess liquidity is primarily responsible. Under this hypothesis, the increase in housing prices is due mostly to inflation; which is the result of an increase in liquidity. This section shows that excess liquidity was generated by the funding and capital privileges of the Government Sponsored Enterprises (GSEs), specifically Fannie Mae and Freddie Mac. This excess liquidity has two sources, borrowing rates and capital requirements.
· A. Excess Liquidity Created by Lower Borrowing Rates
A paper written by W. Scott Frame and Lawrence J. White in the Journal of Economic Perspective explains that “As a result of this perceived implicit guarantee, Fannie Mae and Freddie Mac can typically borrow at interest rates that are more favorable than those of a AAA-rated corporation (though not quite as favorably as the rates on government debt), even though their stand-alone ratings would be about AA- or less. For Fannie Mae and Freddie Mac, empirical studies suggest that this translates into roughly a 35–40 basis point debt funding advantage”.
This means that every time the market borrowing cost decreases, as it did during the 2001-2005 period, the borrowing cost of Fannie and Freddie was also reduced and the 35-40 basis points funding advantage was maintained. Any reduction in the price of money is followed by an increase in demand for money, or demand for liquidity. This is true at an aggregate level and is generally true at a microeconomic level. However, the money demand curve is not linear, it is convex. The convexity of the money demand curve has been confirmed throughout empirical studies (Figure 2).
Figure 2: Money Demand Curve
Figure 2 shows the aggregated money demand curve of the U.S. economy, and is the aggregate of many smaller individual convex money demand curves. One of these is the money demand curve of Fannie and Freddie. When the Federal Reserve lowered its fund rate, all players in the economy increase their money demand. However, because of the very nature of convex functions, Fannie and Freddie adjusted their money demand by more than other players in the economy and in particular by more than what the market would consider appropriate for their risk.
This distortion effect is lower when the economy is closer to its average long term rate, but when rates are very low, as they were between 2001 and 2005, the effect of a small change in rates has an increased effect on liquidity. This went unnoticed in the early 90s, when interest rates were low, because Fannie and Freddie were smaller agencies. However, by 2001, Fannie and Freddie had more than $1 trillion in assets and by 2007, over $6 trillion. These agencies acted as amplifiers of the Federal Reserve Monetary Policy and as they became larger, thereby strengthening the amplification effect. What is more, unlike the liquidity pumped by the Federal Reserve, which diffuses throughout the economy, the liquidity injected by Fannie and Freddie was focused on one specific sector: residential housing.
· B. Excess Liquidity Created by Lower Capital requirement
The 35–40 basis point debt funding advantage is only one part of the amplification effect of these agencies. The other part is the reserve requirements. Banks and other financial institutions are required to hold minimum capital ratios (Figure 4), thus if these institutions wish to increase their leverage, they are limited by this ratio. The capital ratio has a direct effect on the liquidity created by the Federal Reserve’s policy. A lower capital ratio will allow banks to leverage up and lend more and will lead to amplification of the liquidity creation process. Fannie and Freddie had a lower capital ratio requirement than most banks and thus amplified the Federal Reserve’s policy by more than other banks. But unlike banks and other financial institutions who spread this amplification effect throughout the whole economy, Fannie and Freddie focused this effect on the residential housing market (exhibit 5).
A paper published by W. Scott Frame and Lawrence J. White (Emerging Competition and Risk-Taking Incentives at Fannie Mae and Freddie Mac, 2004) raised red flags regarding the use of GSEs. Typically, residential mortgage securitization has a minimum 4% capital/asset requirement. However, Mortgage Backed Securities with an AA- rating or better have only a 1.6% requirement. Since Fannie and Freddie could borrow at AAA- rates, their securitized MBS could benefit from capital requirement advantage. This created an incentive to securitize conforming mortgages.
Note that the distinction between conforming and non-conforming mortgages is important as Fannie and Freddie were only allowed to insure conforming mortgages.
Figure 4: Breakdown of Outstanding Mortgage Debt
As shown in Figure 4, banks are concerned about maintaining a minimum level of capital in order to avoid being put under scrutiny. By contrast, Fannie and Freddie are required to hold only 2.5% capital against their mortgages (Fussing and Fuming over Fannie and Freddie, W. Scott Frame and Lawrence J. White, Journal of Economic Perspectives—Volume 19, Number 2—Spring 2005—Pages 159–184).
Monetary theory is very clear about the impact of capital ratios and liquidity. A decrease in capital ratio creates money, while an increase in the ratio reduces the supply of money in the economy. While officially, a bank only needs 6% of tier-1 capital to be considered well capitalize, they generally exercise conservatism in striving for higher capital ratios than are required by regulation. For example, Goldman Sachs Tier 1 Capital Ratio in the third quarter of 2008 was 11.6% and JP Morgan of 7.91% (Source: Company Website), not too different from its historical ratios (vs. 2.5% for Fannie and Freddie).
The gap between the tier-1 ratio of banks and the ratio of Fanny and Freddie has a significant impact on the amount of liquidity created, which is measured by the multiplying effect of money. For example, an initial deposit of 100 dollars in Goldman Sachs would create nearly $1000 (10x). However, a $100 deposit at Fannie and Freddie would create nearly $4000 (40x). Fannie and Freddie have thus created four times more liquidity than a well capitalized bank.
A lower capital ratio causes the individual money demand curve of Fannie and Freddie to shift to the right. As can be seen in Figure 5, reducing the tier one capital ratio from 8% (banking industry average) to 2.5% (The Fannie and Freddie level) quadruples the demand for liquidity. In other words, if Fannie and Freddie had been deprived of their GSE privileges, they would have demanded (and injected) four times less liquidity than the typical bank.
Figure 6: Money Demand and Capital Ratios
C. Putting it all Together
The following table shows the evolution of the mortgage market in the past six years. The change in the number of outstanding mortgages represents the increase in money demand, or the increase in liquidity. For example, in 2006, $901 billion were added to the stock of mortgages. This is the difference between the mortgages originated and the mortgages released. In this case it is irrelevant to distinguish between origination and securitization because the national stock of mortgages includes both. The change in outstanding mortgages and debt line items show the share of Fannie and Freddie in the net flow of mortgages. In other words, if in 2006 $901 billion was added through the mortgage market, $312 billion were added by Fannie and Freddie and the rest by non-GSEs institutions.
Figure 7: Mortgage Market 2002-2007
As can be seen, nearly $4.99 trillion of liquidity were added in the past six years through the mortgage debt system. Of that, $2.25 trillion was added by Fannie and Freddie and $2.75 trillion by other companies.
Figure 8: Mortgage Liquidity with Federal Fund Rate
Based on the liquidity added by Fannie and Freddy (using the increase in the stock of outstanding mortgages as a proxy) and using the borrowing rate of AAA companies discounted by their 40 bps debt funding advantage it is possible to obtain their Money Demand Curve.
Figure 9: GSE Money Demand Curve
Based on this curve we can calculate the excess liquidity created by the Fannie and Freddies’ special debt funding granted by the implicit backing of the government. For example, we know that the current demand curve is of the type:
The money demand (d) without the premium (p) is:
And the excess liquidity (ε ) created by the lower borrowing cost would would be given by:
In numerical terms, this results in an excess of liquidity of 30% which translates into nearly $1.2 trillion since 1994 (nominal). Note that as the interest rate decreases the impact of the special funding rate is amplified because of the convexity of the money demand curve. Therefore, a drop in the borrowing rate from 7% to 6% would create $58 billion in excess liquidity. However a drop from 6% to 5% creates nearly $143 billion, which explains why most of that $1.2 trillion excess liquidity was pumped into the mortgage system after 2002.
As described, Fannie and Freddie have 2.5% capital ratios (vs. an average 8% for well capitalized institutions). This shifts the money demand curve to the right or multiplies the amount of money by a factor m=4 as previously shown. Thus, the money demand curve equation of Fannie and Freddie without the special capital ratio is:
Factoring the capital ratio into the calculation it is found that Fannie and Freddie pumped nearly $3.1 trillion of excess liquidity into the mortgage market between 1994 and 2007. In other words, 80% of all the money the GSEs injected into the system was available purely because of the implicit backing of the government. A Fannie and Freddie without government intervention would have injected $3.1 trillion less into the mortgage system. Total liquidity pumped into the system since 1994 is approximately 7.4 trillion dollars, out of which $3.1 trillion are pure government subsidy.
An injection of $3.1 trillion is a disruption to any market and does not come without consequence. In the next section we explore how this excess liquidity created price inflation in the housing market.
· D. How Excess Liquidity Created the Housing Bubble
The excess liquidity created by the special status of Fannie and Freddie is equivalent to a demand-side subsidy. This can be illustrated using the IS/LM model in which an increase in liquidity shifts the LM curve to the right and results in a shift of the aggregated demand curve to the right. The final impact on the price of housing will depend on the elasticity of the supply curve. The supply curved can be derived from the housing sales data provided by the National Association of Realtors. The regression of the past 17 years is very accurate (R squared = 0.96) and its elasticity is consistent with the elasticity found by other research. The demand curve is plotted based on the sales made each year so for example, we know that in 1994 nearly 3.5 million homes were sold at a median price of $113 thousand, therefore the demand curve must intersect at that point.
Figure 10: Domestic Home Supply Curve
The explanation for an increase in price and quantity is a shift in the demand curve to the right. Shifts in the demand curve can occur with an increase in income, government subsidies, technologies and changes in expectations.
Securitization and GSEs have injected $7.4 trillion dollars into the system since 1994, an average $528 billion per year. Since the average number of home sold during that period is 5 million, the average injection is $105K per house per year. In other words the liquidity injected by securitization and the GSEs and their excess liquidity accounts for 92% of the price increase in housing.
This result is extremely revealing. Not only does it confirm the conclusions of Mian & Sufi who correctly discarded the income hypothesis and the price expectation hypothesis, but it is also surprisingly robust given the simplicity of the model and given the fact that two different approaches are used (supply demand from the housing market perspective and a monetary approach from the Financial Institutions perspective).
This tool also allows us to differentiate between the increase in price due to the development of the securitization technology and the price increase due to government intervention (reflected in the excess liquidity). As described, the excess liquidity amounts to $3.1 trillion which is equivalent to $44.000 per home per year. This is equal to 41% of the price increase.
This shows that Fannie and Freddie created price inflation by 25% in the housing market by injecting liquidity. Surprisingly, the Case Chiller Index has dropped 22% since its peak in June 2007. This suggests that the price adjustment in housing can be due to the markets internalizing the fact that 20 - 25% of the housing price was pure inflation. This also suggests that the housing market should not continue to fall because of the excess liquidity. However, it could continue to fall because of other dynamics such as income shock or price expectation shock.
It can be argued that Fannie and Freddie are as responsible as the securitization market for creating the bubble, as they account for only 41% of the price increase. However, there has been no bubble in other securitized markets such as auto loans, student loans and credit cards. Moreover, securitized mortgages adjusted much faster than Fannie and Freddie did in the face of the financial crisis. In fact, non-agency lenders began reducing liquidity in 2006 as soon as the Fed Fund Rate began to increase. Fannie and Freddie however continued to aggressively pump liquidity into the system (see Exhibit 7), which is consistent with the convexity of the money demand curve. Finally, the increase in housing price due to securitization cannot be defined as inflation, as it is based on fundamental value creation.
2- Recommendations & Simulation
1- Stop the creation of excess liquidity by eliminating any preferential treatment to Fannie and Freddie and other GSEs.
2- We did not include the excess liquidity created by other agencies such as Ginnie Mae. If they have not, they should be privatized and subject to the same rules and standards than other financial institutions are: same capital ratio, same borrowing rate, no implicit government backing.
3- The government should guarantee what it has committed to, which is the conforming loans on the GSEs balance sheet. The proceeds from selling of state-owned companies could fund this program. We do not recommend using federal funds for this guarantee as it would take taxpayer’s money and thus reduce growth prospect.
4- Eliminate minimum capital requirements. The goal of these requirements was to protect the financial system from collapse and turbulence. This system has failed to protect against modern financial shocks (LTCM, Subprime) and introduces structural rigidity and additional cost to the financial system. Moreover, other check and balance mechanisms are already in place to measure how well-capitalized banks are. Eliminating this requirement will free up much needed capital.
A recent paper by MIT Sloan Professor Jiang Wang and McCombs School of Business Professor Jennifer Huang, (Market Liquidity, Asset Prices, and Welfare, 2008) shows that the number of participants in the market has a direct effect on the profitability of existing players and therefore on their willingness to take risk. Therefore, an increase in the number of players would typically reduce the profitability and the risk taking capability of other players.
As the following simulation shows, by shutting down Fannie and Freddie, or at least by allowing them to stay at non-preferential capital ratios and borrowing rates, policy makers would achieve two important victories. First profitability of existing players should increase and thus their willingness to take more risks. Second, they would eliminate the volatility and inflation in housing prices caused by the presence of Fannie and Freddie.
The following simulation roughly replicates the subprime crisis using the levers described above: money demand curves, house supply curve, corporate bond yields and capital ratios among others. For corporate bond yield we used the AAA, Moody's Seasoned Aaa Corporate Bond Yield from the Federal Reserve of Saint Louis. The simulation starts in 1994 and finishes in year 2007.
We introduced an exogenous shock in 2006, such as the dramatic increase in default rate in subprime mortgages. The result is similar to what happened in reality, money created by non-GSEs dropped dramatically, and then, with a delay, changed the money pumped by GSEs. This replicates fairly well past events. We find however that this model cannot fully explain the drop in housing prices.
The next simulation uses the current situation as a starting point. That is, illiquid markets, lower housing prices and current outstanding mortgages. For simplicity, we assume the same AAA Corporate Bond yield curve as in simulation 1, which explains the cycles. We then implement our recommendations of eliminating special privileges (capital ratios and funding rates) for the GSEs. As shown in the following graphics, the liquidity crisis ends in year four (2012). This can be explained by the Huang and Wang’s competition feedback loop: as institutions make more profit, they take more risk and inject more liquidity. Further, we find that the recovery is much faster with our recommendation because by eliminating unfair competition (the GSEs), the competition loop is more efficient.
This simulation supports our case that the policy change recommendations will lead to a faster economic recovery.
PART III: ACCOUNTING RULES
1- Summary of the Strength and Weaknesses of each accounting Regime
The debate over the value of assets in balance sheets is almost as old as accounting itself. It is not a trivial debate, as balance sheets and income statements are the reflection of the performance and health of a company.
One method of valuing an asset is using the historical cost (HC). Under this method the value of the asset is the acquisition value net of depreciation. One of the advantages of this method is that it is a true value, actual cash was paid for that asset and there is a bill to back that value. The disadvantage of this method is that the book value of the asset can become very different from the liquidation value (market value) of the asset. For example, the General Motors building in Manhattan was built in 1968 and now fully depreciated would have a book value of 0 under the historical cost. If General Motors were to sell that building today it would be at a significant dollar value. This lack of transparency is a cornerstone of the Historical Accounting critic.
Another weakness of historical accounting is that it creates friction in the securities market. For example, a trader can buy a stock for $100 at time zero. Suppose that the stock price is $120 at the closing of period. Under Historical Cost, the trader cannot record that $20 increase as income. Therefore he would have to sell it to record the earnings and if he were to keep it, he would need to buy it again. This creates transaction cost and friction in the market that is inefficient. For long term securities (CDO and MBS) this means also that issuers do not hold the products to maturity, thus creating an incentive to separate the issuer and holder of the security.
Alternatively, mark-to-market accounting proposes recording assets at fair market value. This is attractive as long as there is a publicly quoted market for those assets, such as the stock and bond markets. FASB, the SEC and the IRS have issued new rules regarding the treatment of mark to market in cooperation with the IASB in order to standardize accounting around the world. By the end of 2007 all publicly traded American companies were required to shift to FAS 157.
Fair market value accounting has been credited for adding transparency to the market and for bringing information to investors in a timely manner. Critics, on the other hand, credit it for amplifying the housing crisis and creating the financial meltdown.
Recent academic and industry research has found three major flaws in the Mark to Market Value: increased volatility, reduced welfare, and inefficiency for long term assets.
2- MTM Flaw #1: Increased Volatility
The increased volatility of MTM accounting is best described in a paper published by the Federal Reserve of New York (Liquidity and Leverage, Adrian & Shin, 2008). Adrian & Shin show that when financial institutions have a fixed leverage ratio, they adjust their mark to market balance sheet to increases in asset price by increasing their leverage. This results in procyclical leverage:
Therefore, when assets are marked to market and prices increase, banks tend to buy more assets with debt in order to compensate for their lower leverage ratio. When assets are marked to market and their prices decline, banks become overleveraged and reduce their debt by selling assets, with this selloff having the effect of further reducing asset prices.
In historical cost accounting, changes in the price of securities do not result in changes in the balance sheet. For this reason Adrian & Shin conclude that MTM adds volatility. This also explains the massive selloff observed over the past year; banks sell securities not because they want to, but because they are mandated by regulatory requirements to keep a minimum capital ratio.
3- MTM Flaw #2: Welfare Reduction
The second flaw of MTM is the welfare reduction effect which is caused by the liquidity pricing phenomenon. There is liquidity pricing when an asset is priced not based on its supply and demand curves but on the supply and demand for liquidity; in this case the asset simply becomes a currency that can be exchanged for liquidity. Research shows that this contagion property of MTM results in lower welfare than a historic accounting system. This is especially true in the presence of long term securities and claims. This has been discussed in many papers: Mark-to-Market Accounting and Liquidity Pricing (Allen & Carletti, 2006) and Marking-to-Market: Panacea or Pandora’s Box? (Plantin, Sapra & Shin 2007).
Allen & Carletti show that when liquidity pricing occurs, market accounting is not desirable because prices reflect the availability of liquidity instead of the future earning power of the financial system. They illustrate the contagion effect by modeling a world with investors, insurance companies, banks and real economy firms. The insurance sector insures the asset of the real economy (machinery). The model also assumes three periods (0, 1 and 2). There are two securities available to invest: a short term (with no return) and a long term one (imagine a risk free bond with maturity at time 2).
The insurance company invests its premium in the long term asset. However, if it faces claims in period 1, the insurance company will need to sell the long term asset which implies that someone must supply the liquidity to buy that asset. However, the only way of having liquidity at that period is by investing in short term security which has no return. If no one holds liquidity then the price of the long term asset falls to 0 and the insurance goes bankrupt. The problem arises when the bank is also holding that long term asset. Market to market forces the bank to write that asset down. But at no point the underlying asset has become riskier, it is simply that the lack of liquidity and the bankruptcy of the insurance company has brought it to 0.
The following example is taken from Mark-to-Market Accounting and Liquidity Pricing (Allen & Carletti)
Asset Return = 0
Long Asset Return =R= 1.1
Loan Yield in period 3 with probability β=0.7
Firms demand for loans =
Depositor’s Utility Function = U(c) = Ln(c)
Depositor’s become early consumers with probability λ=0.5
Investor’s opportunity cost = ρ = 1.15
Payment to banks on their loan = b = ρ/ β = 1.64
x = short asset, y = long asset, z = loans
Bank’s objective function:
And the solution would be:
As can be seen, the depositor’s expected utility under historical cost accounting would be 0.0487. When the bank is allowed to share the risk with the insurance company the expected utility is higher at 0.0496. However, when the bank is forced to mark to market the expected utility of the depositors falls to 0.0235 because the bank goes bankrupt and the depositor loses a portion of his deposit.
The conclusion is that Mark to Market accounting can create contagion and force healthy banks to be liquidated unnecessarily, while historical cost does not suffer from these drawbacks. Reality is of course more complex and underlying assets are rarely risk free, yet the model shows that MTM accounting increases systemic risk.
4- MTM Flaw #3: Losses and Duration of Portfolio
The Plantin, Sapra & Shin model arrives at a similar conclusion, but differentiates between the effect on long term and short term balance sheets:
1- For short term assets, MTM reduces the inefficiencies of historical cost accounting, but for long term assets MTM is more inefficient than historical cost accounting
2- For liquid assets, MTM reduces the inefficiencies of historical cost accounting, but for illiquid assets marking to market is more inefficient than historical cost accounting
3- For junior assets, MTM reduces the inefficiencies of historical cost accounting, but for senior assets MTM is more inefficient than historical cost accounting
As they explain:
“We obtain that historical cost accounting generates counter-cyclical trades that smooth the fundamental volatility of the asset, whereas in the mark-to-market regime, the feedback of measurement on pricing is pro-cyclical and increases fundamental risk. It is as if a representative investor had a counter-cyclical risk aversion under a mark-to-market regime, and a procyclical risk aversion under historical cost measurement.”
To prove this Plantin, Sapra & Shin starts by defining the following variables:
They also assume that each manager maximizes the expected
date-1 accounting value of the portfolio. This value depends on the accounting
regime. If Historical Cost then
constant smaller than 1
s=Proportion of financial institutions that have decided to sell their portfolio
γ= is the measure of liquidity of the asset. If γ=0 then market for the asset is infinitely deep.
The model assumes that the FI that have decided to sell their assets are matched randomly (uniform distribution over [0,s]) with buyers. Therefore the proceeds from the sales are:
The left side of the inequality represents the expected value if the FI holds the portfolio, the right side represents the expected value for the FI if it sells. This equation shows that if the portfolio is sufficiently short-lived (d ≤ ½ ) then the FI will prefer to hold the portfolio. Therefore market to market delivers in this case the best solution.
If d ≥ ½ (long lived assets) then the decision depends on the value of v:
A similar model can be built for the Historical Cost accounting regime. Plantin, Sapra & Shin develop a game theory model to find the unique equilibrium outcomes and in order to find the critical values for s. The conclusion of the model is that Historical accounting and Mark to Market accounting are good depending on the term. As can be seen in the graphic, the Historical Cost curve is smoother than the Mark to Market curve (which has a step increase). This is one of the strengths of Historical Accounting.
5- When Accounting Meets Quantum Physics
This leads us to our final conclusion. When financial institutions mark their assets to market, they are in fact extracting information from the market. As the three papers presented have shown, by measuring the market we are also changing the market, which makes it harder to measure. This is a well known phenomenon in quantum physics called the Heisenberg Uncertainty Principle. Heisenberg observed that that it was not possible to measure the position and the momentum of a particle at the same time, that there was a tradeoff between the accuracy of the momentum and that of position.
In other words, it is possible to take the temperature of a bucket of water with a thermometer, but by doing so the thermometer is changing the temperature of the water and so there is a loss of accuracy. We argue that the same happens with financial markets.
The Heisenberg uncertainty principle is expressed by the following equations:
The accuracy of the price of asset is measured by its distance from the
Intuitively we find that a decrease the uncertainty of the
value of P(v) results in an increase in expected losses. The presence of
6- Recommendations & Simulation
Based on these findings we give the following recommendations:
1- Suspend the MTM accounting regime at least for long term assets and replace it with historical cost accounting. The purpose of markets is not to provide valuation information; their function is to provide a meeting point for buyers and sellers. In this sense, MTM is fundamentally flawed.
Inspired by the model developed by Adrian & Shin, we simulated a bank’s balance sheet exposed to different shocks and situations. It is assumed that the bank starts with $100m in securities, $10m in equity and the remainder in debt. The bank’s target debt to equity ratio is 11.1%. We analyzed three scenarios: bullish, neutral and bearish. The stock market returns on the three scenarios are random and normally distributed. They differ in the size of the upside and of the downside. Each scenario is analyzed under different day-to-day stock market autocorrelation assumptions (0 day, 3 days and 7 days of autocorrelation). Each scenario is then put under an external shock (in order to simulate the bankruptcy of a small mortgage bank or an unexpected drop in the fed fund rate).
In the following scenario, markets are normal (expected return = 0, normal distribution). However on day 30 there is an economic shock that cuts returns from day 30 to 100 by an average of 10 points. Two things happen. First, because of the reinforcing feedback loops, MTM creates liquidity pricing and massive selloff, the value of assets drops almost immediately and stays at a low level. Assets under HC absorb the shock much later because the pricing feedback loop is much weaker and there is no selloff. Secondly and most importantly, the bank holding the MTM portfolio goes bankrupt on day 50, 20 days after the beginning of the crisis. The bank with the HC portfolio is able to stay in business. This can be explained by the fact that there is no liquidity pricing (no selloff) under HC and by the fact that HC smoothes volatility over longer periods of time.
Another interesting difference between MTM and HC is its impact on leverage. The following graphic describe a normal scenario with no shocks (such as the one before June 2007). Under the MTM regime, banks increase their liabilities at a much faster rate than they would have done under a HC regime. This is consistent with the conclusions of Adrian & Shin.